This is great. It starts out with a straightforward job that's technically impossible (but, like many technically impossible things, easy to do when near enough is good enough), and leads into an entertaining discussion of mathematical proofs, both accepted and faulty, many of which have a lot more direct application to human life than you might at first think.
See also the gloriously annoying Doctor James Anderson, a computer scientist and garden-variety mathematical crank who's recently attained a certain amount of celebrity for his tireless work in polluting the brains of children with nonsense.
21 December 2006 at 9:27 am
A long time ago, Russell and Whitehead set out to try to prove arithmetic using set theory. In essence, they were trying to rigorously prove that "1+1=2", which isn't as easy as you might think. The result was "Principia", a monument in mathematics.
And somewhere in there is a mistake, because they seem to have done what Gödel said could not be done. No one knows where it is (and no one's willing to do the work to find it) but there's no doubt at all that there is one.
I was involved in a situation similar to one in that article. Certainly not a very important case, to be sure, but interesting nonetheless. About 30 years ago, back when Omni magazine still existed and was actually worth reading, it had its own mathematics column (a reflection of Martin Gardner, I guess). They brought up an interesting and at the time unsolved problem and challenged their readers to solve it:
A large number of hunters are place at random on a plane. At a particular signal, every hunter aims at the hunter who is nearest to him and they all fire simultaneously. Since they're all crack shots who hit and kill who they aim at, what proportion of the hunters will be killed?
Obviously this is probabilistic, but was there a central proportion around which the result would cluster that wasn't a function of the size of the playing field or the number of hunters?
I had access to a superpowerful VAX 750 (ooh!) which I could program in BASIC (aah!) and use pretty much all of for several days during a Christmas-to-New Years shut down. So I wrote a program to do a Monte Carlo simulation, which I ran with 500 hunters, then for 1000, and then for 2000. I plotted histograms of the results which showed that there actually was a single number, and using my last run I was able to determine the value to 3 decimal places.
Turns out that someone else actually derived a real proof. But how was the guy at Omni to determine if their proof was correct? Well, it predicted a number, and the number turned out to agree with the one I had found to the limits of my precision.
So the guys at Omni gave the prize to the other guys. (sob)
21 December 2006 at 6:17 pm
This was linked from the Bad Science article above. It's like reading one of those single page rants on the web with the constantly changing font size and colours and hallucinogenic background gifs. Compulsory reading for anyone interested in law, maths and mental health.
24 June 2013 at 11:52 am
In the several years since this post went up the austlii.edu.au site has been reorganised. And, irritatingly, banned the Wayback Machine in robots.txt, which makes it difficult to tell where the pages are now.
(Standard dead-link-updating trick, for use on normal sites that don't block Web crawlers: You use the Wayback Machine to get the text of the original page, then search for a string from that text - any six grammatical words are surprisingly likely to be unique - to see if there's still a live version of the page somewhere. If there isn't, or if you specifically don't want an updated modern version of the page, you of course just link to one of the archived Wayback versions.)
Aaaaanyway, I found the above excellent transcript again; it's now here:
http://www.austlii.edu.au/cgi-bin/sinodisp/au/cases/cth/HCATrans/2003/641.html
Some more of the same fellow from a few years earlier is here:
http://www.austlii.edu.au/cgi-bin/sinodisp/au/cases/cth/HCATrans/1996/265.html
[whoops - first version of this comment had the same link for both of these]
And I think this may be the same bloke again...
http://www.austlii.edu.au/cgi-bin/sinodisp/au/cases/act/ACTAAT/1999/11.html
...or maybe not, because in this third one he's just making a nuisance of himself over bald tyres on his car, not explaining that the court doesn't exist because two fives don't make ten and the judge is a mosquito net if you divide Ezra Pound by a duck.
22 December 2006 at 12:05 am
You'll be overjoyed to learn that Theodore J. Rout, the bloke who's confusing the judges in the above transcript, does indeed have a Web site, and it is exactly what you'd expect.
I think it's fair to draw an, albeit fuzzy, line between cranks like James Anderson - whose theories are clearly explainable in English, even if they may be logically defective - and people like Theo Rout, who appear to be suffering from a much more serious mismatch between their internal model of the universe and what the rest of us see happening.
Rout's explanations ("the dividing and multiplying by zero, the set that they are adhering to, enables me - it causes things to cease to exist. Now, I have proven everything is on nothing so if everything is on nothing and you multiply it by zero, then the entire universe and the world does not exist. I have proven it conclusively"...) do indeed sound like the ramblings of someone with a delusional disorder, not just someone whose missed a few steps in the proof. It's hard to read Rout's VeryLongPage without having Time Cube flashbacks.
(Further commentary.)